一维前缀和

https://www.acwing.com/problem/content/description/797/

#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N = 1e5  + 15;
int n, k, a;
int s[N];

int main() {
    cin >> n >> k;
    //预处理前缀和
    for(int i = 1; i <= n; i++) {
        cin >> a;
        s[i] = s[i - 1] + a;
    }

    while(k--) {
        int l, r;
        cin >> l >> r;
        cout << s[r] - s[l - 1] << endl;
    }
    return 0;
}

二维前缀和

https://www.acwing.com/problem/content/798/

#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N = 1e3  + 15;
int n, m, q, k;
int s[N][N];

int main() {
    cin >> n >> m >> q;
    //预处理前缀和
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= m; j++) {
            cin >> k;
            s[i][j] = k + s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1];
        }
    }

    while(q--) {
        int x1, y1, x2, y2;
        cin >> x1 >> y1 >> x2 >> y2;
        cout << s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1] << endl;
    }
    return 0;
}

一维差分

https://www.acwing.com/problem/content/799/

#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N = 1e5 + 15;
int n, m;
int a[N], b[N];

int main() {
    cin >> n >> m;
    for(int i = 1; i <= n; i++) {
        cin >> a[i];
        b[i] = a[i] - a[i - 1];
    }
    while(m--) {
        int l, r, c;
        cin >> l >> r >> c;
        b[l] += c;
        b[r + 1] -= c;
    }

    for(int i = 1; i <= n; i++) {
        b[i] += b[i - 1];
        cout << b[i] << " ";
    }
    return 0;
}

二维差分

https://www.acwing.com/problem/content/description/800/

#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N = 1e3 + 15;
int n, m, q;
int a[N][N], b[N][N];

int main() {
    cin >> n >> m >> q;
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= m; j++) {
            cin >> a[i][j];
            b[i][j] = a[i][j] - a[i - 1][j] - a[i][j - 1] + a[i - 1][j - 1];
        }
    }

    while(q--) {
        int x1, y1, x2, y2, x;
        cin >> x1 >> y1 >> x2 >> y2 >> x;
        b[x1][y1] += x;
        b[x2 + 1][y1] -= x;
        b[x1][y2 + 1] -= x;
        b[x2 + 1][y2 + 1] += x;
    }

    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= m; j++) {
            a[i][j] = b[i][j] + a[i - 1][j] + a[i][j - 1] - a[i - 1][j - 1];
            cout << a[i][j] << " ";
        }
        cout << endl;
    }
    return 0;
}